1,721,073 research outputs found
A Semi-Implicit, Semi-Lagrangian Scheme Using the Height Coordinate for a Nonhydrostatic and Fully Elastic Model of Atmospheric Flows
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A cascadic conjugate gradient algorithm for mass conservative, semi-implicit discretization of the shallow water equations on locally refined structured grids
No full textAn efficient nonhydrostatic dynamical core for high resolution simulations down to the urban scale
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The TR-BDF2 method for second order problems in structural mechanics
Full text linkThe application of the TR-BDF2 method to second order problems typical of structural mechanics and seismic engineering is discussed. A reformulation of this method is presented, that only requires the solution of algebraic systems of size equal to the number of displacement degrees of freedom. A linear analysis and numerical experiments on relevant benchmarks show that the TR-BDF2 method is superior in terms of accuracy and efficiency to the classical Newmark method and to its generalizations
Flexible and efficient discretizations of multilayer models with variable density
Full text linkWe show that the semi-implicit time discretization approaches previously introduced for multilayer shallow water models for the barotropic case can be also applied to the variable density case with Boussinesq approximation. Furthermore, also for the variable density equations, a variable number of layers can be used, so as to achieve greater flexibility and efficiency of the resulting multilayer approach. An analysis of the linearized system, which allows to derive linear stability parameters in simple configurations, and the resulting spatially semi-discretized equations are presented. A number of numerical experiments demonstrate the effectiveness of the proposed approach
Unconditionally Strong Stability Preserving Extensions of the TR-BDF2 Method
Full text linkWe analyze monotonicity, strong stability and positivity of the TR-BDF2 method, interpreting these properties in the framework of absolute monotonicity. The radius of absolute monotonicity is computed and it is shown that the parameter value which makes the method L-stable is also the value which maximizes the radius of monotonicity. In order to achieve unconditional monotonicity, hybrid variants of TR-BDF2 are proposed, that reduce the formal order of accuracy, while keeping the native L-stability property, which is useful for the application to stiff problems. Numerical experiments compare these different hybridization strategies to other methods used in stiff and mildly stiff problems. The results show that the proposed strategies provide a good compromise between accuracy and robustness at high CFL numbers, without suffering from the limitations of alternative approaches already available in literature
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